If my source is to be believed Flappers 2 Rappers by Tom Dalzell, "bimbo" meant "great person" in the 1920s'. It wasn't until the 30s' that it was even associated with females.

Sometimes, you just have to laugh at the political incorrectness of early 20th century music. Racism and sexism all over the place! It's so disturbing that it becomes funny!

This recording is a snappy show number from 1920 that is very funny, especially Frank Crummit's rendition of the lyrics. Crummit would remain a singer of humorous songs for the rest of his recording and radio career. He married Julia Sanderson, also a radio personality noted for playing a ukelele, and together they performed on radio into the early 1940's.
I personally enjoyed hearing this song which is also part of my own large 78 rpm record collection.

The title of this song is actually "My Little Bimbo Down On The Bamboo Isle". I've submitted a correction.